Subgroups — C₂×#333 #1541

Order 128.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈	C₂	1	2	yes	maximal
3	#333	C₂	1	4	yes	maximal, direct product factor
4	C₂²×Q₈	C₄	1	2	yes	—
5	C₂²×C₈	—	2	2	no	—
6	C₄⋊Q₈	—	2	2	no	—
7	C₄⋊Q₈	C₄	1	2	yes	—
8	C₄⋊Q₈	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄	—	2	2	no	—
10	C₂×C₄²	C₂²	1	1	yes	characteristic
11	C₄⋊C₈	—	2	2	no	—
12	C₄⋊C₈	C₂²	1	4	yes	—
13	C₂×Q₈	—	2	2	no	—
14	C₂×Q₈	—	4	4	no	—
15	C₂×Q₈	C₂×C₄	1	4	yes	—
16	C₂²×C₄	—	2	2	no	—
17	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄	D₄	1	2	yes	—
19	C₂×C₈	—	2	4	no	—
20	C₂×C₈	—	4	4	no	—
21	C₄⋊C₄	—	2	4	no	—
22	C₄⋊C₄	—	2	4	no	—
23	C₄²	C₂×C₄	1	1	yes	characteristic
24	C₄²	D₄	1	2	yes	—
25	C₄²	C₂³	1	1	yes	characteristic
26	C₂³	C₂²⋊C₄	1	1	yes	characteristic
27	Q₈	—	4	4	no	—
28	Q₈	—	4	4	no	—
29	C₂×C₄	—	2	2	no	—
30	C₂×C₄	—	2	4	no	—
31	C₂×C₄	—	4	4	no	—
32	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄	SD₁₆	1	4	yes	—
35	C₂×C₄	Q₁₆	1	4	yes	—
36	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄	C₂×D₄	1	2	yes	—
38	C₈	—	4	4	no	—
39	C₂²	#100	1	2	yes	—
40	C₂²	#103	1	4	yes	—
41	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	2	1	no	—
44	C₄	—	4	4	no	—
45	C₄	#103	1	4	yes	—
46	C₄	C₂×SD₁₆	1	2	yes	—
47	C₄	C₂×Q₁₆	1	2	yes	—
48	C₂	#333	1	4	yes	direct product factor
49	C₂	C₂×#100	1	1	yes	characteristic
50	C₂	C₂×#103	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #333	C₂	direct (N × H)
48. C₂	#333	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.